Collaborative decoding is an approach that can achieve diversity and combining gain by exchanging decoding information among a cluster of physically separated receivers. On AWGN channels, the least-reliable-bits (LRB) exchange scheme can achieve performance close to equal-gain combining (EGC) of all received symbols from all receivers, while reducing the amount of information that must be exchanged. In this paper, we analyze the error performance of collaborative decoding with the LRB exchange scheme when nonrecursive convolutional codes are used. The analysis is based on the observation that the extrinsic information generated in the collaborative decoding of these convolutional codes can be approximated by Gaussian random variables. A density-evolution model based on a single maximum a posteriori decoder is used to obtain the statistical characteristics of the extrinsic information. With the statistical knowledge of the extrinsic information, we develop an approximate upper bound for the error performance of the collaborative decoding process. Numerical results show that our analysis gives very good predictions of the bit error rate for collaborative decoding with LRB exchange. At high signal-to-noise ratios collaborative decoding with properly chosen parameters can achieve the same error performance as EGC of all received symbols from all receiving nodes.